Emergency Maths Question

[Phil Alderson]

I am trying to study for an exam and one question has me stumped, I should be able to work it out but can't.

Two objects leave a point at the same time, one travelling at 10 m/s and the other at 23m/s an observer sees the first one and then three hours later sees the second. How far away is the origin point?

This should be easy to work out but I just can't get it.

[MK]

First it is best to get all the units straightened out, so  3 hours = 60 x 60 x 3 = 10800 Seconds

Let the car going 10m/s be A and the one at 23m/s be B

As car A arrives at the point 3 hours after B we know it is 108000m behind (10800 seconds x 10m/s)

Lets let X equal the distance car A has already travelled so at the time t when car B passes the observer we can say they have travelled...

for A, X metres and B X + 108000 metres

Distance = Speed x Time so Time = Distance/Speed

So Car A      t = X/10

and Car B t = (X + 108000)/23

As the time for both to reach these respective points is the same we can put both equations equal to eachother so

X/10 = (X + 108000)/23

so

2.3X = X + 108000

1.3X = 108000

    X = 83076... metres

Add this to the distance Car B is ahead (108000) and the origin is therefore 191076m (rounded a little)

To check we can see how long it would take each car to cover this distance, for Car A 191076/10 = 19107.6 or 5.3 Hours

And B 191076/23 = 8307... or 2.3 Hours

[Phil Alderson]

Thanks Tom, A it makes sence now and B the answer we were supplied is wrong.

Phil

[Banshee Ambulance]

Here is a silly little maths thing, It kept me entertained!

Three men each have ten pounds and decide they want to buy a cow. They each give their ten pounds to a fourth man, the middle man, who goes off to buy a cow. The middle man buys a cow for 25 pounds and decides to keep 2 pounds as commission for his services.  He then distributes the remaining three pounds among the three investors, leaving them with 1 pound change each.
Each of the three men has therefore spent 9 pounds and the middle man has kept 2 pounds. 3 X 9 is 27 + 2 = 29 where is the last pound? 

[JimC]

There is no extra pound. The cow cost £25 + £2 Commission = £27.

But pedigree livestock is (or was until very recently: I haven't checked) sold in guineas (1 guinea = 21 shillings = £1.05p) and there will also normally be some luck money from the vendor to the buyer, so livestock purchase is much more complicated than you might think!

[Eggbert]

JimC you are right pedigree cattle are still  sold in guineas and you would usually get luck money but generally only at auction